# Probablity confusion

#### Alexandra

##### New member
On my statistics final I was caught offguard by a simple probability exercise that I just did not know how to do. It stated that 3% of the population has the predisposition for a particular disease. Within this 3%, .99 test positive. Meanwhile, out of the 97% that does not have the predisposition, only. 02 tests positive. It t
hen asked that if someone tests positive, what is the probability that this individual has the predisposition.
It has been bothering me for a day now! I must know how to do this. Heeeelp

#### srmichael

##### Full Member
On my statistics final I was caught offguard by a simple probability exercise that I just did not know how to do. It stated that 3% of the population has the predisposition for a particular disease. Within this 3%, .99 test positive. Meanwhile, out of the 97% that does not have the predisposition, only. 02 tests positive. It t
hen asked that if someone tests positive, what is the probability that this individual has the predisposition.
It has been bothering me for a day now! I must know how to do this. Heeeelp
We don't normally do a problem for someone without seeing any work from the person, but I'm feeling generous today...

$$\displaystyle \displaystyle P(Predis|+) = \frac{P(Predis \cap +)}{P(+)}$$

$$\displaystyle \displaystyle P(Predis \cap +)=(.03)(.99)=.0297$$

$$\displaystyle \displaystyle P(+)=(.03)(.99)+(.97)(.02)=.0491$$

$$\displaystyle \displaystyle P(Predis|+) = \frac{.0297}{.0491}=.6049$$